The authors admire Poincaré’s idea that the convention on the nature for light propagation is the foundation of the measurement of time and point out that the conventions on the light velocity is just the conven...The authors admire Poincaré’s idea that the convention on the nature for light propagation is the foundation of the measurement of time and point out that the conventions on the light velocity is just the convention on the symmetries of space time.The conditions on the transitivity of synchronization of clock rate are shown.With the condition,not only the question about the definition of the synchronization of rate of clocks located at different places is answered,but also find the solution to the definition of the equality of two durations is found.展开更多
我们为应该接着导致全球一致估计并且应该在参数上特别地在他们的依赖的学习帮助的纺纱加权的球状的波浪功能的现在的新不可分的方程。为有 m = 的延长球状的波浪函数 0，在那里存在其内核是的不可分的方程(罪恶 x ) 大数学意义的 /x，...我们为应该接着导致全球一致估计并且应该在参数上特别地在他们的依赖的学习帮助的纺纱加权的球状的波浪功能的现在的新不可分的方程。为有 m = 的延长球状的波浪函数 0，在那里存在其内核是的不可分的方程(罪恶 x ) 大数学意义的 /x，和 sinc 函数内核(罪恶 x )/xis。我们也扩大类似的 sinc 功能核(罪恶 x )/x 到盒子 m 别等于 0 并且 s 别等于 0，它有趣地作为某种 Hankeltransformations 生产。展开更多
The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions＇ eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of al...The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions＇ eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of all its terms is obtained. This means that the spheroidal problem is solved completely in the way for the ground eigen-value problem. The shape invariance property is proved retained for the super-potential and subsequently all the excited eigen-value problem could be solved. The results show that the spheroidal wave equations are integrable.展开更多
In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight st...In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersymmetric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.展开更多
The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in...The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained： （a） the Rindler spacetime as a whole is not stable; （b） the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; （c） there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that： （a） perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; （b） the Schwarzschild black hole as a whole might be really unstable; （c） the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.展开更多
The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Sch...The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole （r 〉 2m） and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.展开更多
文摘The authors admire Poincaré’s idea that the convention on the nature for light propagation is the foundation of the measurement of time and point out that the conventions on the light velocity is just the convention on the symmetries of space time.The conditions on the transitivity of synchronization of clock rate are shown.With the condition,not only the question about the definition of the synchronization of rate of clocks located at different places is answered,but also find the solution to the definition of the equality of two durations is found.
基金Supported by the National Natural Science Foundations of China under Grant Nos 10475013, 10373003, 10375087, and 10375008, the National Basic Research Program under Grant No 2004CB318000, and the Post-Doctor Foundation of China.
文摘我们为应该接着导致全球一致估计并且应该在参数上特别地在他们的依赖的学习帮助的纺纱加权的球状的波浪功能的现在的新不可分的方程。为有 m = 的延长球状的波浪函数 0，在那里存在其内核是的不可分的方程(罪恶 x ) 大数学意义的 /x，和 sinc 函数内核(罪恶 x )/xis。我们也扩大类似的 sinc 功能核(罪恶 x )/x 到盒子 m 别等于 0 并且 s 别等于 0，它有趣地作为某种 Hankeltransformations 生产。
基金Supported by the National Natural Science Foundation of China under Grant Nos 10875018 and 10773002, and the National Basic Research Program of China under Grant No 2010CB923200.
基金Supported by the National Natural Science Foundations of China under Grant Nos 10475013, 10373003, and 10375087, the National Key Basic Research Programme of China under Grant No 2004CB318000.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10875018 and 10773002.
文摘The perturbation method in supersymmetric quantum mechanics is used to study the spheroidal wave functions＇ eigenvalue problem. The super-potential are solved in series of the parameter α, and the general form of all its terms is obtained. This means that the spheroidal problem is solved completely in the way for the ground eigen-value problem. The shape invariance property is proved retained for the super-potential and subsequently all the excited eigen-value problem could be solved. The results show that the spheroidal wave equations are integrable.
基金supported by the National Natural Science Foundation of China (Grant No. 10875018)
文摘In this paper, we combine the perturbation method in supersymmetric quantum mechanics with the WKB method to restudy an angular equation coming from the wave equations for a Sehwarzschild black hole with a straight string passing through it. This angular equation serves as a naive model for our investigation of the combination of supersymmetric quantum mechanics and the WKB method, and will provide valuable insight for our further study of the WKB approximation in real problems, like the one in spheroidal equations, etc.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10475013, 10375087 and 10373003）, the National Basic Research Program （Grant No 2004CB318000） and National Science Foundation for Post-Doctoral Scientists of China.
文摘The stability problem of the Rindler spacetime is carefully studies by using the scalar wave perturbation. Using two different coordinate systems, the scalar wave equation is investigated. The results are different in the two cases. They are analysed and compared with each other in detail. The following conclusions are obtained： （a） the Rindler spacetime as a whole is not stable; （b） the Rindler spacetime can exist stably only as part of the Minkowski spacetime, and the Minkowski spacetime can be a real entity independently; （c） there are some defects for the scalar wave equation written by the Rindler coordinates, and it is unsuitable for the investigation of the stability properties of the Rindler spacetime. All these results may shed some light on the stability properties of the Schwarzschild black hole. It is natural and reasonable for one to infer that： （a） perhaps the Regge-Wheeler equation is not sufficient to determine the stable properties; （b） the Schwarzschild black hole as a whole might be really unstable; （c） the Kruskal spacetime is stable and can exist as a real physical entity; whereas the Schwarzschild black hole can occur only as part of the Kruskal spacetime.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10475013, 10373003 and 10375087）, the National Basic Research Program （Grant No 2004CB318000） and the Post-Doctor Foundation of China.
文摘The stability of the Schwarzschild black hole is restudied in the Painlevé coordinates. Using the Painlevé time coordinate to define the initial time, we reconsider the odd perturbation and find that the Schwarzschild black hole in the Painlevé coordinates is unstable. The Painlevé metric in this paper corresponds to the white-hole-connected region of the Schwarzschild black hole （r 〉 2m） and the odd perturbation may be regarded as the angular perturbation. Therefore, the white-hole-connected region of the Schwarzschild black hole is unstable with respect to the rotating perturbation.
基金Supported by the National Natural Science Foundations of China under Grant Nos 10373003, 10475013 and 10375087, and the National Key Basic Research of China under Grant No 2003CB716300.
